There are many physical problems which seem to be quite simple although the corresponding mathematical models are rather complicated to be studied, analyzed and solved. Computer simulations are often used and, in some classrooms or educational facilities, computer graphics and mathematical representations may be the only experiences or devices to which students are exposed. Therefore, there is a need for dynamic teaching aids that allow students to interact with the physical world and increase their intuitive understanding.
Particularly, it should be noted that, in 1794 Rev. George Atwood invented an apparatus known as an “Atwood Machine.” See (Tipler, Paul A. (1991), Physics for Scientist and Engineers, Third Edition, Extended Version. New York: Worth Publishers. ISBN 0-87901-432-6. Chapter 6, example 6-13, page 160). The “Atwood Machine” was the first reasonably successful invention of an inertial mass motion teaching aid. It consists of two bodies attached to opposite ends of a massless inextensible wire wound round a massless frictionless pulley. Each body can move only along a vertical axis.
The proposed invention can be considered a modified “Atwood Machine”. It was chosen because it is a simple mechanical system with one degree of freedom and can easily show a body's acceleration by: a=(m2−m1)/(m2+m1) g, where m1 and m2 are the body's mass and g is the gravitational acceleration.
The proposed invention disclosed herein is used to visually demonstrate the net linear motion of the frame of an Impulse Driver, where m1 is the mass of the Impulse Driver and m2 is a mass of a counterweight, which in some embodiments, can be, but is not limited to, a container of sand, for example. The mass of the Impulse Driver and the mass of the counterweight in some embodiments and implementations can be of equal weight. Additionally two pulleys are used to avoid any contact between the Impulse Driver and the counterweight.
Persons knowledgeable of Atwood Machines will be familiar with a similar mechanism known as a Swinging Atwood Machine (Moody, Parker W. (2013). “Modeling a Swinging Atwood Machine,” Journal of the Advanced Undergraduate Physics Laboratory Investigation: Vol. 1:Iss. 1, Article 1) where one of the masses is allowed to swing in a two-dimensional plane, producing chaotic motions for some system parameters and initial conditions.
The Impulse Driver of at least some embodiments of the present invention is mechanically restrained from swinging away from the vertical by four (or other number of) guide posts placed concentrically around the frame.